Question

Two point charges lie on the x axis. A charge of 9.3 μC is at the origin, and a charge of -4.1 μC is at x = 10 cm .

At what position x would a third charge q3 be in equilibrium?

Would it matter whether it is positive or negative?

Thank you, and if possible could you show detailed work, I can get halfway through this problem and then I get stuck.

Answer 1

The required position has to be near the charge of smaller magnitude and on the side of smaller charge so the two charges exert force in opposite direction.

Let it be x.

At this location, electric field will be zero.

Using Colombs law with q in uC and x in cm,

kq1/x^2 + kq2/(x- 10)^2

9.3/x^2 -4.1/(x-10)^2

x =29.76 cm

No, it would not matter because when electric field will be zero, force will also be zero independent of charge.